Question: Rewrite as a simplified fraction. ${0.81\overline{2} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 812.2222...\\ 100x &= 81.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 731}$ ${x = \dfrac{731}{900}} $